$Extension of laplace transform to multi-dimensional fractional integro-differential equations$

Extension of laplace transform to multi-dimensional fractional integro-differential equations

The main focus of this thesis is to extend the study of one-dimensional fractional to multi-dimensional fractional calculus and study of multi-dimensional Laplace transformation with their respective applications. This extension will be used to solve special types of multi-dimensional fractional cal...

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Main Author:	Ahmood, Wasan Ajeel
Format:	Thesis
Language:	English
Published:	2017
Subjects:	Laplace transformation
Online Access:	http://psasir.upm.edu.my/id/eprint/70908/1/FS%202017%2042%20IR.pdf
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id	my-upm-ir.70908
record_format	uketd_dc
spelling	my-upm-ir.709082019-08-07T04:43:24Z Extension of laplace transform to multi-dimensional fractional integro-differential equations 2017-05 Ahmood, Wasan Ajeel The main focus of this thesis is to extend the study of one-dimensional fractional to multi-dimensional fractional calculus and study of multi-dimensional Laplace transformation with their respective applications. This extension will be used to solve special types of multi-dimensional fractional calculus such as space-time partial fractional derivative. The multi-dimensional Laplace transforms method used to solve the multi-dimensional fractional calculus with constant and variable coefficients and the multidimensional modification of Hes variational iteration method to solve the multi-dimensional fractional integro-differential equations with non-local boundary conditions are developed. The study of multi-dimensional space-time fractional derivative with their applications and also, new fractional derivative and integral including Riemann-Liouville having a non-local and non-singular kernel are detailed. Finally, we obtained the exact solution of multi-dimensional fractional calculus, space-time partial fractional derivative and the system of matrix fractional differential equation in Riemann- Liouville sense of matrices but there are some problems that cannot be solved analytically, thus we solved them by multi-dimensional variational iteration method. This study shows that integral transform can be used to present new solutions to problems by certain applications for solving them. Laplace transformation 2017-05 Thesis http://psasir.upm.edu.my/id/eprint/70908/ http://psasir.upm.edu.my/id/eprint/70908/1/FS%202017%2042%20IR.pdf text en public doctoral Universiti Putra Malaysia Laplace transformation
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Laplace transformation
spellingShingle	Laplace transformation Ahmood, Wasan Ajeel Extension of laplace transform to multi-dimensional fractional integro-differential equations
description	The main focus of this thesis is to extend the study of one-dimensional fractional to multi-dimensional fractional calculus and study of multi-dimensional Laplace transformation with their respective applications. This extension will be used to solve special types of multi-dimensional fractional calculus such as space-time partial fractional derivative. The multi-dimensional Laplace transforms method used to solve the multi-dimensional fractional calculus with constant and variable coefficients and the multidimensional modification of Hes variational iteration method to solve the multi-dimensional fractional integro-differential equations with non-local boundary conditions are developed. The study of multi-dimensional space-time fractional derivative with their applications and also, new fractional derivative and integral including Riemann-Liouville having a non-local and non-singular kernel are detailed. Finally, we obtained the exact solution of multi-dimensional fractional calculus, space-time partial fractional derivative and the system of matrix fractional differential equation in Riemann- Liouville sense of matrices but there are some problems that cannot be solved analytically, thus we solved them by multi-dimensional variational iteration method. This study shows that integral transform can be used to present new solutions to problems by certain applications for solving them.
format	Thesis
qualification_level	Doctorate
author	Ahmood, Wasan Ajeel
author_facet	Ahmood, Wasan Ajeel
author_sort	Ahmood, Wasan Ajeel
title	Extension of laplace transform to multi-dimensional fractional integro-differential equations
title_short	Extension of laplace transform to multi-dimensional fractional integro-differential equations
title_full	Extension of laplace transform to multi-dimensional fractional integro-differential equations
title_fullStr	Extension of laplace transform to multi-dimensional fractional integro-differential equations
title_full_unstemmed	Extension of laplace transform to multi-dimensional fractional integro-differential equations
title_sort	extension of laplace transform to multi-dimensional fractional integro-differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2017
url	http://psasir.upm.edu.my/id/eprint/70908/1/FS%202017%2042%20IR.pdf
_version_	1747812933937659904

Extension of laplace transform to multi-dimensional fractional integro-differential equations

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